Question
A local bank recommends opening a savings account with a $100 initial deposit and a $15 monthly deposit. A local credit union recommends opening a savings account with a $50 initial deposit and a $20 monthly deposit. A system of equations is written to find the month at which the two accounts have the same balance. If x represents the number of months after the initial deposit and y represents the account balance in dollars, the equation for the credit union account balance is y = 20x + 50. What is the equation for the bank account balance?(1 point)
The equation for the bank account balance is y=
.
The equation for the bank account balance is y=
.
Answers
Answer
Which system of equations is indicated by this description?
x increased by 3 is equal to the product of 2 and y.
5 times y is equal to negative x minus 10.
(1 point)
Responses
{x+3=2y5y=−x−10
enlarged left brace start layout first row x plus 3 equals 2 y second row 5 y equals negative x minus 10 end layout
{x+3=2+y5y=−x−10
enlarged left brace start layout first row x plus 3 equals 2 plus y second row 5 y equals negative x minus 10 end layout
{x+3=2y5y=x−10
enlarged left brace start layout first row x plus 3 equals 2 y second row 5 y equals x minus 10 end layout
{3x=2y5y=−x−10
x increased by 3 is equal to the product of 2 and y.
5 times y is equal to negative x minus 10.
(1 point)
Responses
{x+3=2y5y=−x−10
enlarged left brace start layout first row x plus 3 equals 2 y second row 5 y equals negative x minus 10 end layout
{x+3=2+y5y=−x−10
enlarged left brace start layout first row x plus 3 equals 2 plus y second row 5 y equals negative x minus 10 end layout
{x+3=2y5y=x−10
enlarged left brace start layout first row x plus 3 equals 2 y second row 5 y equals x minus 10 end layout
{3x=2y5y=−x−10
Answer
Use the image to answer the question.
Two parallel lines slope upward on a coordinate plane. A dotted line passes through the plotted point left parenthesis 0 comma 0 right parenthesis. A solid line intersects the y-axis at left parenthesis 0 comma 3 right parenthesis.
Write the equations for the system of linear equations graphed.
(1 point)
The equation of the solid line is y=
, and the equation of the dotted line is y=
.
Two parallel lines slope upward on a coordinate plane. A dotted line passes through the plotted point left parenthesis 0 comma 0 right parenthesis. A solid line intersects the y-axis at left parenthesis 0 comma 3 right parenthesis.
Write the equations for the system of linear equations graphed.
(1 point)
The equation of the solid line is y=
, and the equation of the dotted line is y=
.
Answered by
GPT-4o mini
To find the equation for the bank account balance at the local bank, we will use the information given:
- The initial deposit is $100.
- The monthly deposit is $15.
The account balance can be expressed in a linear form, where \(y\) is the account balance and \(x\) is the number of months after the initial deposit. The formula for the bank account balance will be:
\[
y = \text{initial deposit} + (\text{monthly deposit} \times \text{number of months})
\]
Substituting in the values:
\[
y = 100 + 15x
\]
So, the equation for the bank account balance is:
\[
y = 15x + 100
\]
- The initial deposit is $100.
- The monthly deposit is $15.
The account balance can be expressed in a linear form, where \(y\) is the account balance and \(x\) is the number of months after the initial deposit. The formula for the bank account balance will be:
\[
y = \text{initial deposit} + (\text{monthly deposit} \times \text{number of months})
\]
Substituting in the values:
\[
y = 100 + 15x
\]
So, the equation for the bank account balance is:
\[
y = 15x + 100
\]
Answered by
GPT-4o mini
Based on the description provided, we are looking for a system of equations that captures the two statements:
1. "x increased by 3 is equal to the product of 2 and y."
2. "5 times y is equal to negative x minus 10."
We can translate these statements into equations:
1. The first statement can be expressed as:
\[
x + 3 = 2y
\]
2. The second statement can be expressed as:
\[
5y = -x - 10
\]
Combining these, we have the system of equations:
\[
\begin{cases}
x + 3 = 2y \\
5y = -x - 10
\end{cases}
\]
So the correct response based on your options is:
\[
\{ x + 3 = 2y \\ 5y = -x - 10 \}
\]
1. "x increased by 3 is equal to the product of 2 and y."
2. "5 times y is equal to negative x minus 10."
We can translate these statements into equations:
1. The first statement can be expressed as:
\[
x + 3 = 2y
\]
2. The second statement can be expressed as:
\[
5y = -x - 10
\]
Combining these, we have the system of equations:
\[
\begin{cases}
x + 3 = 2y \\
5y = -x - 10
\end{cases}
\]
So the correct response based on your options is:
\[
\{ x + 3 = 2y \\ 5y = -x - 10 \}
\]
Answered by
GPT-4o mini
To derive the equations for the two lines based on your description, let's break down the details:
1. **Solid Line:**
- The solid line intersects the y-axis at the point (0, 3). This is the y-intercept, so the equation will have the form:
\[
y = mx + b
\]
where \( b = 3 \) (the y-intercept).
- You mentioned there are two parallel lines that slope upward. Therefore, the slope \( m \) will be some positive value. Let's assume the slope of the solid line is \( m \) (you would need to refer to the image to determine the exact value).
- Thus, the equation for the solid line will be:
\[
y = mx + 3
\]
(Replace \( m \) with the exact value of the slope if you have it from the image.)
2. **Dotted Line:**
- The dotted line passes through the origin (0, 0), which means the y-intercept is 0. Therefore, its equation will also have the form:
\[
y = mx + b
\]
where \( b = 0 \).
- Again, since it is parallel to the solid line, it will have the same slope \( m \).
- Hence, the equation for the dotted line will be:
\[
y = mx
\]
(Replace \( m \) with the exact slope value.)
In conclusion, your equations will be:
- The equation of the solid line is:
\[
y = mx + 3
\]
- The equation of the dotted line is:
\[
y = mx
\]
Make sure to replace \( m \) with the precise slope from the graph if you have that information.
1. **Solid Line:**
- The solid line intersects the y-axis at the point (0, 3). This is the y-intercept, so the equation will have the form:
\[
y = mx + b
\]
where \( b = 3 \) (the y-intercept).
- You mentioned there are two parallel lines that slope upward. Therefore, the slope \( m \) will be some positive value. Let's assume the slope of the solid line is \( m \) (you would need to refer to the image to determine the exact value).
- Thus, the equation for the solid line will be:
\[
y = mx + 3
\]
(Replace \( m \) with the exact value of the slope if you have it from the image.)
2. **Dotted Line:**
- The dotted line passes through the origin (0, 0), which means the y-intercept is 0. Therefore, its equation will also have the form:
\[
y = mx + b
\]
where \( b = 0 \).
- Again, since it is parallel to the solid line, it will have the same slope \( m \).
- Hence, the equation for the dotted line will be:
\[
y = mx
\]
(Replace \( m \) with the exact slope value.)
In conclusion, your equations will be:
- The equation of the solid line is:
\[
y = mx + 3
\]
- The equation of the dotted line is:
\[
y = mx
\]
Make sure to replace \( m \) with the precise slope from the graph if you have that information.
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